Habit formation and Interest-Rate Smoothing

Following a conjecture of Kozicki and Tinsley we generalises the habit formation model of consumption to allow for both a multiplicative utility function and a habit\aspiration function which is a geometrically weighted average of past consumption. The geometric form of the aspiration function addresses the recent concerns of Wendner (2002) who shows that a combination of a multiplicative utility function and an aspiration function that is an arithmetic weighted average of past consumption violates some important assumptions of utility theory. The geometric form allows us to derive an optimising model of the IS-PC form in which there is a greater degree of inertia in both inflation and output that arises from the role given to habit formation. The geometric form also allows us to derive a rule for the interest rate in which there is equivalent inertia in the interest rate. Because the welfare function of the policymaker is that of the representative agent, the optimal rule penalises changes in income and also responds sluggishly to shocks. This goes some way to accounting for the common observation that the responses of output and inflation to shocks are drawn out, and the interest rate used for policy is persistent. We calibrate the model and find that we can replicate the persistence in interest rate setting by a monetary authority over and above that attributable to the persistence in inflation and the output gap.